The mirror cube is an interesting puzzle that is very similar to the 3x3 but functions in a slightly different way. The mirror cube works by having pieces with different heights instead of different colours. It was probably initially called the mirror cube because it was made with silver or gold coloured stickers which appeared to mirror slightly, however, more recent mirror cubes such as the one from Gan have actually had different coloured stickers/pieces. What is true for all mirror cubes though, is that they all have one colour on all the sides.
The mirror cube may initially seem harder to solve than a regular 3x3 because it is easy to get overwhelmed and confused when the pieces don't look the same, however, the solving method is the exact same as a regular 3x3 so in theory it is no harder than the 3x3.
The algorithm to solve the mirror cube is just the same as the regular 3x3, you can first solve the cross, I would recommend starting on the lowest or highest side first, you can then insert the first two layers, although if you are solving it for the first time I would recommend just doing it layer by layer even if you do use F2L for normal 3x3 solving, you can then move onto OLL and PLL and try to recognise as much as you can of the cases, it is all about training your brain with lateral thinking, there may be no colours but what patterns match? Where are the blocks of pieces you would normally recognise?
So is the mirror cube worth it? Absolutely! If you want to expand your cube collection and try out a range of new and interesting puzzles then the mirror cube should be high up your wishlist, you can also consider trying other mirror cubes such as the 2x2 mirror (and get confused when you think you have got a twisted corner but you DO NOT) or if you fancy something more difficult, then why not try the 4x4 mirror, again, it is just the same as solving a regular 4x4!
One final challenge to consider is solving the mirror cube blindfolded. Since the pieces are all different heights, these height differentials can be felt with your fingers, meaning that it is possible to solve the mirror cube blindfolded with no inspection.
If you want to solve the mirror cube fast then all you need to do is practice it. The current world record for mirror cube average of 5 is held by Braden Richards with an average of 11.23 seconds.
I also solved the 4x4 mirror cube blindfolded when I first got one, before even seeing the puzzle itself, I had already scrambled it and solved it!