Another surd

Algebra Level 3

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

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


This is one part of the set Fun with exponents
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