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