I've Definitely Seen it Before

Geometry Level 4

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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