Cat City/WMG

The mice from Planet X are somehow connected to the mice seen in movies like The Great Mouse Detective, The Secret of NIMH and An American Tail.
Somehow the ancestors of the mice (and the cats for that matter) got on Earth and then the intelligent mice and cats reproduced and spread their seed in intelligent mice and cats that look surprisingly like the native species'. On the other hand, you could say that all the intelligent versions of animals that don't have human like brains came from Planet X, but then again, HOW THE FUCK! Could they all get there?
 * Don't forget The Rescuers and Chipand Dale Rescue Rangers.

Planet X is the future Earth from the movies mentioned above.
Intelligent mice, rats and cats inhabited always inhabited the Earth, living in a Mouse World. Then due to some catastrophe, humanity went extinct, so the intelligent animals didn't need to keep up The Masquerade anymore.

Planet X is Earth after The Brain managed to conquer it.
Related to the previous idea: The catastrophe that led to humanity's extinction was the Brain's successful attempt to Take Over the World.