\[A=\dfrac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\]

If \(A\) can be expressed as \(a+b\sqrt{c}\) for non-negative integers \(a,b,c\) with \(c\) square free, then find the value of \(a+b+c\).

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