Extreme rationalizing 2

Algebra Level 4

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

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 \(a+b+c\).