Let \( f \) be a polynomial function such that \( \log_{2}(f(x))=\big[\log_{2}\!\big(2+\frac{2}{3}+\frac{2}{9}+\ldots \infty\big)\big]\cdot \log_{3}\!\left(1+\frac{f(x)}{f(1/x)}\right) \), \( x>0 \) and \( f(6)=37 \). Then \( \displaystyle\sum_{n=1}^{10} f(n) \) is equal to ______.
