Red or blue Loctite?
Broken bolts are my bread and butter, I have to get a LOT of them out in my line of work.
The way I get out bolts that are broken off flush is to weld a nut to them. Don't try to weld the nut directly to the bolt (vent liner), you want to build up a small bead on the end of the bolt, then sit the nut down over the bead and fill the nut with weld. You want to get the nut as hot as you can without it melting. The heat from the nut will expand the bolt, breaking it loose. When it's cold it should screw right out.
I do this a LOT.
This works with blue Loctite, but if it's red it might be a problem.