Seems easy huh?

Algebra Level 4

If \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c} = a+b+c ,\) then \(\dfrac{1}{(2a+b+c)^2}+\dfrac{1}{(2b+a+c)^2}+\dfrac{1}{(2c+a+b)^2} \leq \dfrac{x}{y},\)

where \(x,y\) are coprime integers. Find the value of \(x+y.\)

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