How to remove a stuck wiring Snake?

I've managed to get a Snake stuck in ribbed conduit. I managed to get about 15 feet of the snake in the tube before it stopped advancing and now I can't get it out.

How can I remove it without damaging anything?

Without sacrificing the existing wiring in the line there's very little you can do here that doesn't risk damaging what's in the conduit. Best suggestion I have is to twist the snake 1/4 turn left and right while working it back and forth to see if it will break free. You can also try Dyna-Blue or something similar, but that's best applied before trying the pull...

On occasions like this it is sometimes better to cut the snake and declare it a loss rather than risk destroying the existing wires and having a real repair project on your hands.