Cevians in Disguise

In $\triangle ABC$ with area $120$, cevians $AD$, $BE$, $CF$ (with $D$ on $BC$, $E$ on $CA$, $F$ on $AB$) satisfy $\frac{AF}{FB}=1$, $\frac{BD}{DC}=2$, $\frac{CE}{EA}=3$. These cevians pairwise intersect to form a small inner triangle. Find the area of that inner triangle. The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.