Algebra or Geometry

Algebra Level 4

It is given that \( 2\cos \dfrac{2\pi}{n} = x+\dfrac{1}{x}\) for \(n \in \mathbb N\). If \( x^{n} + \dfrac{1}{x^{n}} = an^{b} \), where \(a\) and \(b\) are real numbers, find \(a+b\).