There are definitely pre-packaged adventures that start at level 11.
That said, I've always found that building my own adventures is more rewarding. My suggestion for doing so is to build the campaign in such a way that there is an inflection point, which usually happens off screen - unbeknownst to the players - that sets a ball rolling. This is usually, but not always a villain doing or planning something villainous.
As an example, in the last campaign arc I ran, the wife of one of the local nobles was an impostor. She was an agent sent by the Githyanki to break 6 ancient seals with protected the land from invasion from other planes. This particular part of the world was an area where a bunch of magical ley lines converged, and the seals were placed at particular junctions of these lines. The countess hired the players to destroy these seals, but lied to them about their mission. They were told that they were in fact repairing the seals.
So they went off on adventure after adventure to break these seals, and I put clues in front of them that these seals maybe weren't actually sealing, by doing things like sucking them through a portal after they "repaired" them. But they didn't put the clues together, until eventually they came across the guardian of the 4th seal, who was being very cagey with them, and through conversation, he told them that the seals were supposed to be a certain color when sealed, and the party realized they were turning them a different color.
At this point they decided to turn around and confront the villain, but made the mistake(?) of going through a forest which was destroyed by a calamity in the past (also related to these seals) in which the barrier between the material plane and the feywild was almost non-existent. They spent a week traversing the forest, and when I had them roll a die to see the time-dilation results of their feywild excursion, they got a really bad roll that resulted in days becoming months, so now 6 months have passed in the real world since they set off.
During this 6 months, the villain moved her plan forward with another adventuring party that I had set up as rivals to the players. These adventurers were 100% loyal to the Countess and knew what was really happening. So instead of the final confrontation being something which stopped the Countess from destroying the seals (my original expectation when setting up the arc in the beginning), the final confrontation ended up being at the site of the portal, and it opening on the party as they were trying to stop it from happening by killing the githyanki around the site.
So the party got sucked into the Astral Plane, had some encounters, and eventually ran into an Astral vessel with the Countess (now in her true Githyanki form) and the rival adventuring party on it. They fought and killed them, and then plane shifted out of the Astral Plane.
That's where the arc ended, and now I'm working on the follow-up, which will involve dealing with the mess that has now occurred.
But back to the process of setting up a campaign - I typed all that out above because I wanted to explain how the campaign got to be what it became. I started with the Villain and her plan. Once that was established, I worked out a rough sketch of where I expected things to go, based on three possibilities.
1 - The party follows along with the obvious path presented to them
2 - The party actively goes against the obvious path presented to them
3 - The party completely ignores the obvious path presented to them
And once I come up with those, I try to decide if all three of those possibilites are fun.
1 - The party follows the countess to the end and open the portal - fun
2 - The party learns they are being duped, and try to stop the plan - very fun, and almost what happened
3 - The party goofs off on some other treasure-hunting adventures and ignores the countess (or accidentally loses 6 months in the feywild) and a giant portal to the Astral Plane opens, and Githyanki and Red Dragons pour into the world creating a huge mess - The most fun and what actually happened. I'm currently outlining the follow-up campaign as I type this.
If your premise doesn't seem fun in all three contexts, well, it's time to workshop some ideas to make it fun in all three. You don't have to build out all the details of each branch. You only really need detail for the first couple sessions worth of material. Build the immediate adventure, know what the Villain(s) are planning, and who the major players are.
Everything past the first couple sessions is just a rough outline, since if your players are anything like mine you never know what they will decide to do. Once you know what the driving issue is behind the campaign, it becomes easy to adjust to player actions when they stray from the main thread. (That BBEG isn't just going to sit in his dungeon waiting for the players to come kill him. He has plans. Have him act on those plans in ways that affect the party.)
For the campaign described above, I started with the town they would be working out of, Created the Countess, Count (unwitting bystander) and Captain of the Guard (who was also an unwitting bystander) who was the direct liason between the players and the Countess.
I decided that there would be 6 seals, and decided they they would be themed to Air, Earth, Water, Fire, Light and Dark. I placed them in the world such that Air, Water, and Light would be accessible overland, while Earth, Fire and Dark would all require a trek into the Underdark. I decided that all of them would be guarded by good or neutral creatures(except the final one deep in the Underdark, which had already been corrupted by the Drow), but the early ones would be difficult or impossible to communicate with. I only designed the Air "dungeon" to begin with, since that was the first one the party would be hired to destroy.
And that's all you really need to start up a campaign arc. An overall tension, and an immediate adventure with a handful of important NPCs. The rest can be filled in as you go. I didn't know when I started that the Countess was going to be a Gith. My original idea was an Erinyes, but the Gith idea became a lot more appealing after the trip to the feywild put Option 3 on the board. Also, Mordenkainen's Tome of Foes came out around then which reminded me how cool Gith are.
You can also go with a more simple setup where you send the characters on a discrete adventure every session and they aren't really connected in any tangible way, but I find it much more interesting to build something that takes a long time to become clear to the players. They also seem to really enjoy it.
. So I'd suggest ToA but starting near the city where they can discover the death curse and go deal with it?
