Let F:[3,5] → R be a twice differentiable function on (3,5) such that F (x)= e^-x ∫_3^x(3 t^2+2 t +4 F^′( t )) dt. If F^′(4)=(α e^β-224)/((e^β-4)^2),…

Let $\displaystyle \mathrm{F}:[3,5] \rightarrow \mathbf{R}$ be a twice differentiable function on $\displaystyle (3,5)$ such that $\displaystyle \mathrm{F}(x)=\mathrm{e}^{-x} \int_3^x\left(3 \mathrm{t}^2+2 \mathrm{t}+4 \mathrm{~F}^{\prime}(\mathrm{t})\right) \mathrm{dt}$.If $\displaystyle F^{\prime}(4)=\frac{\alpha e^\beta-224}{\left(e^\beta-4\right)^2}$, then $\displaystyle \alpha+\beta$ is equal to \_\_\_\_.