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.]

In order for the hands of left and right handed clocks to be in the same positions at the same time, one
of two things can be true:

(1) the hour hands are in the same place, and the minute hands are in the same place. This happens only at
6:00 and 12:00.
(2) the hour and minute hands are swapped. This requires the hour and minute hands to form a mirror-image
pair through the vertical bisector of each clock face.

For case 2, at a time of A hours and B minutes past noon, the hour hand will be pointing between 
the A and A+1, B/60 of the way past the hour. The minute hand will be at B/5. We need A + B/60 + B/5 = 12, 
because one hand must be as far past the 12 as the other one needs to reach it. So A + 13B/60 = 12. 
For each A from 0 to 11 you can find a solution; A=12 gives the 12:00 solution already found in the first part.
For A = 0, 13B/60 = 12, or B = 720/13 = 55 and 5/13, for a time of 12:55 and 5/13.
For A = 1, 13B/60 = 11, or B = 660/13 = 50 and 10/13, or a time of 1:50 and 10/13.
For A = 2, 13B/60= 10, B = 600/13 = 46 and 2/13, for the time 2:46 and 2/13.
Likewise we get 
3:41 and 7/13, 
4:36 and 12/13, 
5:32 and 4/13, 
6:27 and 9/13, 
7:23 and 1/13, 
8:18 and 6/13, 
9:13 and 11/13, 
10:09 and 3/13, and 
11:04 and 8/13.

0:55:23
1:50:46
2:46:9
3:41:32
4:36:55
5:32:18
6:27:41
7:23:4
8:18:27
9:13:50
10:9:13
11:4:36