In the expansion of ${\left( {\sqrt[3]{2} + \frac{1}{{\sqrt[3]{3}}}} \right)^n},n \in \;{\rm{N}}$ , if the ratio of ${15^{{\rm{th }}}}$ term from the beginning to the ${15^{{\rm{th }}}}$ term from the end is $\frac{1}{6}$, then the value of $^n{C_3}$ is
