Coefficients from Shared Polynomial Roots

The three roots of $f(x) = 2x^3 - 3x^2 + 4x + 5$ are also three of the roots of $g(x) = 6x^5 + 7x^4 + px^3 + qx^2 + rx + 8$. What is the value of $p + q + r$? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.