SMO 2011 Problem 5

Find all pairs of positive integers $(m,n)$ such that $m+n-\frac{3mn}{m+n}=\frac{2011}{3}.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.