That looks pretty busted up, and I'm guessing you want to fix it,
and making it stronger than it was it more inportant than making it look good as new.
MDF and chipboard are weak in edge-grain, so for durable connections screw into (and preferable through) the faces not into the edges.
What you do is get some 20mm x 2mm aluminum angle that's as long as the join, and some chip-board screws.
Place the aluminium inside the failed corner, drill small holes (eg 1/16" or 1.5mm) through the "wood" into (and through) the aluminium then screw through that hole. do that though both pieces in every 2" or so along the join.
There'll be sharp screw points through the aluminium, but chripboard screws are hard steel, so if you bend them a bit you can break them off fairly easily (eg using pliers)