I have this exact problem, actually, with just the tip of the plug being stuck deep in there. This is a common issue, and I'm sick of seeing the same bad (but well-intended! I know...) advice, so here goes the bad news:
1) On a Macbook, the soundboard thing does not have a hole for you to push the broken piece out from the inside. In other words, opening your Mac up is absolutely NOT "definitely worth it if you have the skills" or such. Your skills don't mean anything here.
2) Unfortunately, this holds true for the Apple people too. The only thing they're allowed to do, with or without warranty, is replace the whole logic board. This costs nearly as much as the whole laptop. So don't even bother asking.
After many google searches, I found one potential solution. I've tried superglue, tweezers, etc. But, one person has said that he succeeded by taking 2 pins with the tips bent and working the broken piece out. Haven't tried it yet myself, but will soon. Anyway, it has to be pulled out, and Apple won't help you here.