"Spoooooooky" Russian rational expressions 2

Algebra Level 3

\[ \mathscr{E} = \sqrt{ \dfrac{ \dfrac{ab + b^2}{3} }{\dfrac{b^3}{3a}} + \dfrac{a+b}{b} } \]

If \( a = 2016 \) and \( b = 2017 \), and \( \mathscr{E} \) can be represented in the form \( \dfrac{x}{y} \), where \(x\) and \(y\) are coprime positive integers, find \(x+y\).


Credit: My former Trig teacher's worksheet of Russian rational expressions
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