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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