Left-Handed Times

A "left-handed" clock has its numbers printed counter-clockwise and runs counter-clockwise to point at them, effectively performing as a mirror image to a normal clock.  Between noon and midnight, at what times are the hands of a left-handed clock pointing in exactly the same directions as those of a regular clock (comparing only hour and minute hands, which may be swapped.)

Source: Original.  [You may ignore any effect due to the electromagnetic weak force.]

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