Dont sweat it If you broke the latch, it doesn't make a shits difference, just remove the plug. Based on the amount of trouble you're having getting that thing out, do you really think it needs a latch to further fasten it? Also if you feel like it's a little loose once you plug it back in ,you can put a dab of hot glue on it.
You could look for a video on this ,but it would be like looking for a video on screwing in a lightbulb.
If it's still fighting you even though the latch is gone now, heat it up with a hairdryer and then do like I said with the pliers and gently rock it
This isnt by chance a prebuilt PC is it? Sometimes they glue the plugs