Is any of the bolt exposed outside of the hole? The thing about bolts is that all of the tension is on the head. Once it snaps off, a lot of the time it's rather easy to screw the rest out of the hole. If there's any, even the littlest bit, exposed, try to turn it by pressing on it with a screwdriver or something. It could be a time consuming process getting all of the angles to actually turn the bolt but it could save you a lot of time in the end.
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