Oh man.....that is going to be a challenge.
What i have HEARD has worked in the past,,,,,,,superglue.
and you have to PRECISE with the application of it......if any of it gets around the connection is forever in there.
But the idea is to use the tiniest amoutn of Sglue, and glue the broken piece back to the piece lodged in the laptop.
Wait for it to dry, and then it will just pull it right out.
YOu dont HAVE to use the brokenm cable to glue on the end of the lodged in piece.......toothpicks work great here too.
Use a tiny TINY amount of glue and glue the end of a toothpick to the lodge in piece, wait for dry, and then pull it out.
But again......you must be extremely careful not to get glue ANYWHERE else but on the lodged piece ONLY.