Im not sure how much access to it you have... but I would drill a hole into the broken off piece slightly smaller than the diameter of the bolt, then hammer in an allen wrench that is slightly bigger than the hole you drilled. Then you can use the allen wrench to remove the rest of the bolt.

It worked for me several times on things I have broken just depends on how tight the rest of it is in there... you may have to completely drill it out and re-tap the hole.