I think that using anchors, already mentioned, is the best solution. Besides the already mentioned answers, there are many different options available to you:
Drill an 8mm hole in the bracket and use a 7 mm screw into the 6mm hole.
Drill another hole in the bracket that is about a centimeter or so away from the original hole and insert a screw through that hole. Generally, the hole in the bracket should be 1 or 2 mm larger than the diameter of the screw.