A lucky nest to call home ....

Algebra Level 4

\[S = \displaystyle\sqrt{9 - \sqrt{\dfrac{13}{9} + \sqrt{\dfrac{13}{81} - \sqrt{\dfrac{13}{6561} + \sqrt{\dfrac{13}{43046721} - .......}}}}}\]

If \(S = \sqrt{\dfrac{a}{b}}\) where \(a, b\) are both primes, find \(a + b\).