If the sum of the first \(20\) terms of the series \(\frac{4.1}{4+3.{1}^{2}+{1}^{4}}+\frac{4.2}{4+3.{2}^{2}+{2}^{4}}+\fr…

If the sum of the first \(20\) terms of the series \(\frac{4.1}{4+3.{1}^{2}+{1}^{4}}+\frac{4.2}{4+3.{2}^{2}+{2}^{4}}+\frac{4.3}{4+3.{3}^{2}+{3}^{4}}+\frac{4.4}{4+3.{4}^{2}+{4}^{4}}+\ldots\) is \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(m+n\) is equal to

[JEE Main 2025, 4 Apr (Shift 2)]