JEB
Legend
No, you don't.
Divide the target HP by (average per die + Con Modifier)...
Simple algebraic solving for Y.
So, let's say you want 221-235 (CR11), and you have a medium critter (thus d8's), and Con 22 (for +6)...Hd = Thp / (Apd + Conmod)
Hd = 235 / (4.5 + 6)
Hd = 235/10.5 = 22.38.
So, we give it 22 HD, and 22x10.5 = 220+11=231hp
Ah man, you got me all excited that there was an easy way, but I just tried it... with Con 22 and 22 HD, it's 22d8+132, and that approach does get an average result of 231 HP... but a maximum result of 308 HP, which should be CR 16, not 11.

That said, I think you're onto something, since that's precisely 5 CR off, and trying it with a few other combinations were similarly off...