How to remove a broken tub stopper ?

Hello, I need to replace my tub stopper. The current stopper operated like this - I need to pull it up and rotate to open , and rotate it again to close the drain. The problem is that the stopper (top part) has broken off (the part has corroded)
So, I got a new one (the full assembly) to replace. I thought I can unscrew the old stopper with a long-nose plier by holding the "shaft" inside the stopper and unscrew it. But, the shaft also broke. So, I just have clean hole now, with nothing to hold and unscrew !
Please advice on what I can do to remove the old stopper assembly out.
Thanks
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Get what is called an "Easy Out." Spiral gadget that fits in a hole with a left-handed thread. You use a tap wrench, and turn counter- clockwise. They come in sizes, and a set of them -- any good hardware or automotive shop has them -- doesn't cost much. They will save your a.. more than once. For things like broken off screws -- you drill a small hole in the center, and fit the easy-out. You already have the hole. Also, try some penetrating oil on the stuck parts, and maybe a little heat from a propane torch, if appropriate. Get a bigger hammer <grin>.
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Thanks !. I will try that.
I will look for a big enough "Easy Out".
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