Cevian Ratio Chase

In $\triangle ABC$, cevians $AD$, $BE$, $CF$ (with $D$ on $BC$, $E$ on $CA$, $F$ on $AB$) are concurrent. Given $\frac{BD}{DC}=\frac23$ and $\frac{CE}{EA}=\frac45$, compute $\frac{AF}{FB}$. The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.