Find $n$ in the binomial $\big[\sqrt[3]{2} +\large\frac{1}{\sqrt[3]{3}} \big]^n$ if the ratio of $7^{th}$ term from the beginning to the $7^{th}$ term from the end is $\large\frac{1}{6}$

Question

$\begin{array}{1 1}(A)\;9\\(B)\;6\\(C)\;12\\(D)\;\text{None of these}\end{array}$