I had snapped one of mine earlier too, I folded a sheet of aluminum foil until it was thick and sturdy then formed it around the bend/snap (this provided protection and support), let it hang a little loose and misted the inside and left it alone.. week later it was just a solid clump of plant inside the "cast" and looks good as new.
Exactly, I am pretty ruff on plants. I have snapped a few branches almost clean of the main stock before. I have used sting, pop-cycle sticks, duck tape, and other items to hold that branch tight in place. Every single one of them made it. Like Fuzzotany said, there will be a nodgual of plant growth where it had healed.
But it sounds like you totally removed it from the plant. So in you case I would take a straight pin and ruff up the broken off piece, and then cut a slit in the original plant, then place a dab of rooting hormone in the slit, and stick the other piece in place, then wrap in snug with string. AND THEN PRAY for the graph to take. This is just an idea, I have never even tried this Idea, but what the hell.