If the sum of the first \( 10 \) terms of the series \( \dfrac{1}{1+1^{4}\times 4}+\dfrac{2}{1+2^{4}\times 4}+\dfrac{3}{1+3^{4}\times 4}+\dfrac{4}{1+4^{4}\times 4}+\cdots \) is \( \dfrac{m}{n} \), \( \gcd(m,n)=1 \), then \( m+n \) is equal to:
\( 256 \)
\( 264 \)
\( 276 \)
\( 284 \)
