Head phone jack

We had the wonderful experience of the tip of our headphones breaking off inside our Macbook. Apple says, in order to fix, they must replace the logic board for $755. Obviously, that would be insane, since the Macbook costs $950. We've tried putting glue on the tip of a toothpick to attempt to get it out, with no luck. Everything functions normally, other than we have no sound, which is annoying. Has anyone else experienced this and had any success with a recovery method?

Thanks!
Mark

Usually Super Glue works what glue did you use?