Hey bounty,
I personally have never worked with CF but have done research into it.
It's worked the same as fiberglass, you'd need to get some CF matt, resin etc. and overlap your break over and under. The repair will act like a microscopic suspension bridge on both sides of the break to keep it from flexing either way. You won't be able to just glue or epoxy the break because its the fibers of the CF combined with the resin that gives the structure strength. You might be able to find some at boat repair shops or other fiberglass type business since they go hand in hand sometimes.
There are different weights, fiber count, thicknesses and resin types just like fiberglass so you might want to do some research on the net to get familiar with the process.
For your small job it might be cheaper to have someone repair it or count it as a loss.
Good luck!