Solve the equation \(x(3x^{2}-19)=2(x^{2}-11)\). If the roots of the equation are in the form of \(a\), \(\frac{r\pm\sqrt{m}}{k}\). Find the value of \(a+r+m+k\).

Note that while expressing your answer in the form given above to get the values of the four variables, the fraction must be in the simplest form (terms)

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