250 Followers Problem - Dedicated to my friend

Geometry Level 5

\[\large A = \left(5,3 \right) ; B = \left(1 , 9 \right)\]

\(A\) and \(B\) are two points on \(xy\)-plane. Let \('M'\) be a point on the line \(L \equiv 2x+3y - 6 =0\) such that \(AM +BM\) is minimized. The coordinates of \(M\) are \(\left(x, y \right)\). Find the value of \(x+y\).

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