A twice differentiable function \(f(x)\) is defined for all real numbers and satisfies the following conditions :

\[\begin{cases} f(0)=2 \\ f'(0)=-5 \\ f''(0)=3 \end{cases} \]

The function \(g(x)\) is defined by \(g(x)={ e }^{ ax }+f(x)\) for all \(x\in R\), where \(a\) is a constant.

If \(g'(0)+g''(0)=0\), then find the possible values of \(a\).

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