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Geometry Level 5

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 $\large \frac{BX}{XC}= \frac{3}{4}$ .

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