Cable broke in iPad port

I would second taking it to the apple store. Let’s say you manage to get it out with a pair of needle nosed tweezers, but you put some scratches around the port doing so. A few months from now you have issues with that port. Even though those scratches are cosmetic in nature and didn’t damage anything they could still be cited as ‘proof’ of existing damage and used as a reason to not repair any future issues.

If the lighting end piece can be removed intact, you should be OK. If you are uncomfortable trying to remove it, make an appointment at an Apple Store or an Authorized service provider and see if they can remove the broken piece.

Actually, you might be better off taking it in fo rservice than trying to do it yourself in case there was additional damage done when it broke.