Let \( f:\mathbb{R}\to\mathbb{R} \) be a function defined by \( f(x)=\dfrac{2e^{2x}}{e^{2x}+e} \). Then \( f\!\left(\frac{1}{100}\right)+f\!\left(\frac{2}{100}\right)+f\!\left(\frac{3}{100}\right)+\ldots+f\!\left(\frac{99}{100}\right) \) is equal to \( \_\_\_ \).
