Question 15
Tetrahedron $ABCD$ has $AD = BC = 28,$ $AC = BD = 44,$ and $AB = CD = 52.$ For any point $X$ in space, define $f(X) = AX + BX$ $+ CX + DX.$ The least possible value of $f(X)$ can be expressed as $m\sqrt{n},$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m + n.$