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 $a+b+c$ .