If the sum of the first $20$ terms of the series $\dfrac{4\cdot1}{4+3\cdot1^{2}+1^{4}}+\dfrac{4\cdot2}{4+3\cdot2^{2}+2^{4}}+\dfrac{4\cdot3}{4+3\cdot3^{2}+3^{4}}+\dfrac{4\cdot4}{4+3\cdot4^{2}+4^{4}}+\cdots$ is $\dfrac{m}{n}$, where $m$ and $n$ are coprime, then $m+n$ is equal to: