Solve it Algebraically? I won't dare

Algebra Level 4

ex+1=α \large e^{ -| x | }+1= \alpha

If the range of values of α\alpha for which the above equation has no solution can be expressed as (,A](B,) \left( -\infty ,A \right] \cup \left( B,\infty \right) , then find the value of A+BA+B .

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