Root 2014?!

Level pending

If

\[x=1+\sqrt[2014]{2}+\sqrt[2014]{4}+\sqrt[2014]{8}+\dots+\sqrt[2014]{2^{2013}}\]

Then, the value of \((\frac{x+1}{x})^{95}\) can be expressed in the form \(\sqrt[b]{2^a}\), where \(a\) and \(b\) are positive coprime integers. What is the value of \(a+b\)?

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