Let $A=a_0+a_1+a_2+a_3+a_4+a_5+a_6 = 1$, where $a_0,a_1,a_2,a_3,a_4,a_5,a_6$ are real numbers. The new operation $\Delta$ is defined as $x\Delta y = x-y$. If:  $$A \Delta a_1 = \frac12$$  $$A \Delta a_2 = \frac23$$  $$A \Delta a_3 = \frac78$$  $$A \Delta a_4 = \frac{29}{30}$$  $$A \Delta a_5 = \frac{139}{144}$$  $$A \Delta a_6 = \frac{839}{840}$$  If $a_0 = \frac{m}{n}$ in its simplest form, find the value of $m+n$. 
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