Just Minimize the Function!

Algebra Level 3

Let $f$ be a real function such that $f(x) = \sqrt[3]{x^2-x+1}$ for $x$ is real number. What is the minimum value of the function $f$?

If this minimum value can be expressed as $\sqrt[a]{\dfrac bc}$, where $a,b,c$ are positive integers, with $b$ and $c$ being coprime integers and $a$ minimized, submit your answer as $a+b-c$.

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