In triangle $ABC$, the medians $AD$ and $CF$ have lengths $36$ and $54$ respectively, and $AB=48$. Extend $CF$ to intersect the circumcircle of $ABC$ at $K$. The area of triangle $CBF$ is $m \sqrt n$, where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any number. Find $m+n$.