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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