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 \(a+b+c+d\).


This is one part of the set Fun with exponents
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