Unfortunately, there's not enough hard evidence to support the claim that dark matter resides in other dimensions. All we know for sure is that, based on our current understanding of physics, the observable universe behaves as if it has more mass than what we are capable of detecting.
You might want to check out a very interesting non-linear spinor theory[1] which contains a chapter on dark matter and dark energy analytically explaining the formation and inner structure, as well as the ratio of dark matter and dark energy throughout the development phase of the universe.
