"Spoooooooky" Russian rational expressions 2

Algebra Level 3

E=ab+b23b33a+a+bb \mathscr{E} = \sqrt{ \dfrac{ \dfrac{ab + b^2}{3} }{\dfrac{b^3}{3a}} + \dfrac{a+b}{b} }

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


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