Wall cabinet bracket & cabling

I've got 2 single wall cabinets (not joined to any others) but 1 of the brackets on each side will sit on top of a cable chase

Can I get away with using a mounting rail and screwing it through as close to the edge as possible and maybe adding a few more across the rail for additional support or is it likely to bend at the unscrewed edge?

Any other suggestions?

Cheers