Just observed my laptop, it seems you have to take it apart, remove all screws, pry that thing with a screwdriver, get to the jack and melt the right leads to take it out. Solder and put all back as it was.
Was cleaning exhaust fan the other day, basically had to do everything above. Biggest pain was plugging back in paper thin bus wires. Hope they are longer then mine on your laptop.
As for soldering, i just repaired power adopter plug which fell from the table. Had to replace old crappy steel wires on flexible copper ones. Everything went smooth. No need to buy new adopter.
Explore your laptop, it would be rewarding time when you get it back to operating condition.