I've Definitely Seen it Before

In $\Delta ABC$ of area equal to $1024$ square units, points $X$, $Z$, and $Y$ divide the line segments $\large \overline {BC}$, $\large \overline {CA}$, and $\large \overline {AB}$ in the ratio $\large 3:4$, $\large 5:6$, and $\large 1:2$. The ratio of areas of $\Delta XYZ$ and $\Delta ABC$ can be expressed as $\Large \frac{m}{n}$, where $m$ and $n$ are coprime positive integers.Determine the value of $m+n$.

Details- When I say $X$ divides $\large \overline {BC}$ in the ratio $\large 3:4$, I mean that $\large \frac{BX}{XC}= \frac{3}{4}$.