If the co-efficient of x^9 in (α x^3+1/(β x))^11 and the co-efficient of x^-9 in (α x-1/(β x^3))^11 are equal, then (α β)^2 is equal to ____.

If the co-efficient of $\displaystyle x^9$ in $\displaystyle \left(\alpha x^3+\frac{1}{\beta x}\right)^{11}$ and the co-efficient of $\displaystyle x^{-9}$ in $\displaystyle \left(\alpha x-\frac{1}{\beta x^3}\right)^{11}$ are equal, then $\displaystyle (\alpha \beta)^2$ is equal to $\displaystyle \_\_\_\_$.