In the expansion of \({\left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)}^{n},\mathrm{n}\in \mathrm{N}\), if the ratio of \…

In the expansion of \({\left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)}^{n},\mathrm{n}\in \mathrm{N}\), 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:

[JEE Main 2025, 4 Apr (Shift 1)]