Find the studs and drill thru stud, after carefully measuring the position of the mounting bracket, and attach the bracket using a minimu 3/16 inch toggle bolt. You will have a very secure installation. By the way, if you can't find two studs to span the bracket, make sure you use the stud you can find and toggle bolts in the drywall at the other end
Another method is to use the same toggle bolts but bolt a sheet of plywood that is about twice the size of the existing bracket. Then using metal Sheetrock screws be sure to hit the studs every six inches or so. Paint the plywood the same color as the wall or bracket then screw the bracket in using the toggle bolts through both the plywood and the wall. It will never move.
Have a nice 4th
Gary