Aluminum is not magnetic

I don’t think it is easy. Most of the other garbage will just tag along when you lift the metals. It would be different if the garbage was burned. Then you could just get the metals out of the ashes. But to have a clean incineration, the temperature will be high enough to evaporate some metals too.

Maybe if you ground all garbage to a powder it could work too. But that is another step that costs time and energy.