Square it later

Algebra Level 4

\[x^{4}+\sqrt{x^{2}+2016}=2016\] The above equation has 1 positive real solution which can be written as \(\sqrt{\dfrac{\sqrt{a}-b}{c}}\), where \(a,b,c\) are positive integers with \(a\) square-free. Find the value of \(\dfrac{a+b+c}{c^{c}}\)

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