Level pending

In equation $$a^b=(a-1)!+1$$ , find $$\sum(a+b)$$.

[ Post your solution. Let's see whether we can evade LTE again.

In your solution, let me know whether I have revealed the keystone by mentioning LTE and reduced the fun of this problem. In this case, I may cease mentioning lemmas or theorems I used. You may refute anything. ]

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