Ok, in the "real" world, this would be impossible because the human body isn't built to run that fast (muscle damage, problems with friction, etc.)
But since D&D nowhere resembles the real world, we'll just say that it's possible, and leave it at that. I mean, if you accept magic, and dragons, and the undead, surely you can accept this.
As for it being broken, I don't see it. Sure, you can move REALLY fast. To what end, though? Despite your speed, you still start your turn depending on your initative roll. No matter how fast you run past enemies, they still get their AoOs. You can run into trouble, just as fast as you can run out of it. A wizard or a sorcerer with Dimension Door or Teleport could go farther than a monk in one round. And last, if Dash and Run is how you want to spend your feats, then god bless ya.