Define \(f(x)=e^{x+1}-1\). Find the sum of all of the values of 'n' that makes g(x) differentiable over the real numbers.

\(g(x)=100\left| f(x) \right| -\sum _{ k=1 }^{ n }{ \left| f(x^{ k }) \right| } \quad (n\in \mathbb{N}\))

(This was the last question in the CSAT Mathematics Type B from this year)

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