# Root of the problem

Algebra Level 4

$\large \frac{\sqrt{5-\sqrt{21}}}{\sqrt{32-2(5-\sqrt{21})} - \sqrt{21}}$

If the value of the radical expression above equals to $$\sqrt{\dfrac{a}{b}} - \sqrt{\dfrac{c}{d}}$$, where $$a,b,c$$ and $$d$$ are positive integers with $$\gcd(a,b) =$$ $$\gcd(c,d) = 1$$. Find $$a+b+c+d$$.

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