Algebra Level 4

$\large \dfrac{1}{a^{2}+9} + \dfrac{1}{b^{2}+9} + \dfrac{1}{c^{2}+9}$

Given that $$a,b$$ and $$c$$ are positive reals with a sum of 1. If the maximum value of the above expression can be expressed as $$\dfrac{x}{y}$$ where $$x$$ and $$y$$ are coprime integers, find the value of $$x+y$$.

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