Let \( F:(3,5)\to \mathbb{R} \) be a twice differentiable function on \( (3,5) \) such that \( F(x)=e^{-x}\displaystyle \int_{3}^{x}\big(3t^{2}+2t+4F'(t)\big)\,dt \). If \( F'(4)=\dfrac{\alpha e^{\beta}-224}{\left(e^{\beta}-4\right)^{2}} \), then \( \alpha+\beta \) is equal to _________.
