Let α>0, be the smallest number such that the expansion of (x^(2/3)+2/x^3)^30 has a term β x^-α, β ∈ N. Then α is equal to ____.

Let $\displaystyle \alpha>0$, be the smallest number such that the expansion of $\displaystyle \left(x^{\frac{2}{3}}+\frac{2}{x^3}\right)^{30}$ has a term $\displaystyle \beta x^{-\alpha}, \beta \in \mathbb{N}$. Then $\displaystyle \alpha$ is equal to $\displaystyle \_\_\_\_$.