Let the sum of the maximum and the minimum values of the function $f\left(x\right)=\frac{2{x}^{2}-3x+8}{2{x}^{2}+3x+8}$ be $\frac{m}{n}$, where $\gcd (m,n)=1$. Then $m+n$ is equal to:

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Let the sum of the maximum and the minimum values of the function \(f\left(x\right)=\frac{2{x}^{2}-3x+8}{2{x}^{2}+3x+8}\…

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