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Use Turtle Wax Ice, it will not leave any residue on black surfaces....
Just the toothbrush will not remove the dried wax because the surface is a rough texture.
Use a toothbrush and some "Black Again" liquid, the stuff you use on your cars rough textured moldings, etc. Even with this, you do have to scrub awhile to get the residue off...
I'm sure there are other products that will remove the dried wax but assure whatever you use, will not lighten or discolor the black surface.