Another surd

Algebra Level 3

$\large \sqrt{11 + \sqrt{21}}$

The above expression can be expressed as $\sqrt{\dfrac{a}{b}} + \sqrt{\dfrac{c}{d}}$ , where $a,b,c$ and $d$ are positive integers with $\gcd(a,b) = \gcd(c,d) = 1$ . Find $a+b+c+d$ .

Another surd

This is one part of the set Fun with exponents