If the sum of the first \( 10 \) terms of the series \( \dfrac{4 \cdot 1}{1 + 4 \cdot 1^{4}} + \dfrac{4 \cdot 2}{1 + 4 \cdot 2^{4}} + \dfrac{4 \cdot 3}{1 + 4 \cdot 3^{4}} + \ldots \) is \( \dfrac{m}{n} \), where \( \gcd(m, n) = 1 \), then \( m + n \) is equal to __________.
