\[\begin{equation} \large \int_0^1\frac{x^{21}}{\sqrt{x^2-x+1}}\,dx \end{equation}\]

The value of the integral above has a closed-form that can be expressed as \[\dfrac{a}{b}-\dfrac{c}{d}\ln3\] where \(a,b,c\) and \(d\) are positive integers with \(\gcd(a,b) = \gcd(c,d) = 1\). Find \(a+b+c+d\).

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