If you can get hold of the frayed end with pointy pliers you're off to a good start. Pull the cable while you flick the release shifter a few times (not all the way straight up) & you should be able to feed it back through the hole enough to thenn allow it to ratchet all the way back. That will push the ball-end out of its holder enough to be able to pull it out.
Sounds easy, but it WILL take a lot of persistence.
Just ride the bloody thing and enjoy yourself!