I used a safety pin (bigger one, about 1.5"), and pushed the pointed pin at the side, pushing the latch that holds the connector on the side.
I just keep doing this on either side, and pull back again. One time after pushing it deep inside, when i pulled it, that side of the broken piece lifted up. So I knew it was possible.
kept doing this until one time the broken piece turned 90 deg. so then i was able to use a thin long nose and pull it out. The whole trial process took ~ 30 mins, with breaks in between. Good thing is since i did that on the sides only, the connector is still ok, and charging still. Just be patient. And yes, at times the pin would bend ...
good luck !