2017 AIME II Problem 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.