Is $\displaystyle x = (\sqrt{2 + 3^{1/5}} + 7^{1/3})^{1/6}$ a rational number? Prove your answer.

I know it isn't and that I need to rewrite $\displaystyle x$ in the form $\displaystyle a_{0} + a_{1}x + ... + a_{n-1}x^{n-1} + a_{n}x^{n} = 0$, but I'm having trouble doing so.