Personally I think that the galaxy rotation problem, and consequently the bullet cluster problem, is a relativistic effect and no dark matter exists.
I.e. the existing visible matter warps space in such a way that it increases the rotation speed of the galaxy.
Any mass in space warps the space around it. It is proven again and again, with gravitational waves being the latest proof.
So a very simple explanation is gravity from the mass of the galaxy warps space in such a way that mass around it seems sped up.