Rational or Irrational?

\(\text{Let } n>1 \text{ be an integer.How many irrational numbers } 'a' \text{ exists such that}\)

\(\sqrt[n]{a+\sqrt{a^{2}-1}}+\sqrt[n]{a-\sqrt{a^{2}-1}} \text{ is rational?}\)

This is a part of my set "Beautiful.. It is!!" .
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