$\large 1+\dfrac{1+7}{1!} + \dfrac{1+7+7^2}{2!} + \dfrac{1+7+7^2+7^3}{3!} +\cdots$

If the above sum can be represented in the form of $\dfrac{ae^a-e}{b}$, then find the value of $a+b$.

$$

**Clarification:** $e \approx 2.71828$ denotes the Euler's number.