It's easiest if you first separate the bracket from the rubber mounts, then grab all the wires of a cable firmly, making sure they all have the same amount of slack, then slowly pull. It's okay to pull on the wires if the force is spread out evenly across all of them. What you don't want to do is pull on one wire more than the rest.
To plug it back in, I first reattach the mounting bracket, then use tweezers to position the plug into the socket opening, then use a flat screwdriver to push the plug all the way home.