Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of \( \left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^{n} \), in the increasing powers of \( \frac{1}{\sqrt[4]{3}} \) be \( \sqrt[4]{6}: 1 \). If the sixth term from the beginning is \( \frac{\alpha}{\sqrt[4]{3}} \), then \( \alpha \) is equal to