Radicals are complicated(2)

Algebra Level 5

\[ \frac{1}{\sqrt{2016x-\sqrt{2016x}}}-\frac{1}{\sqrt{2016x+\sqrt{2016x}}} = \frac{1}{\sqrt{2016x-1}}\]

If the sum of all real root(s) of the above equation is of the form \(\large \frac{1}{y}\).

Find \(y\).

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