I've Definitely Seen it Before

Geometry Level 5

In ΔABC\Delta ABC of area equal to 10241024 square units, points XX, ZZ, and YY divide the line segments BC\large \overline {BC}, CA\large \overline {CA}, and AB\large \overline {AB} in the ratio 3:4\large 3:4, 5:6\large 5:6, and 1:2\large 1:2. The ratio of areas of ΔXYZ\Delta XYZ and ΔABC\Delta ABC can be expressed as mn\Large \frac{m}{n}, where mm and nn are coprime positive integers.Determine the value of m+nm+n.

Details- When I say XX divides BC\large \overline {BC} in the ratio 3:4\large 3:4, I mean that BXXC=34\large \frac{BX}{XC}= \frac{3}{4}.

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