Not many solutions? Part 2

Algebra Level 3

Let the functions $$f(x)$$ and $$g(x)$$ be $$f(x)=x^{3}-2x^{2}+x-2$$ and $$g(x)=x^{2}+1$$ .

Find the sum of all real solutions to the equation

$$f(x)+g(x)=0$$.

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