$$-\frac{2}{5}(\frac{10}{13}-x)+(\frac{2}{13}+x)=6\frac{11}{13}$$
$x=5$
$$-26\left(\frac{10}{13}-x\right)+10+65x=5\left(6\times 13+11\right)$$
$$-26\times \frac{10}{13}+26x+10+65x=5\left(6\times 13+11\right)$$
$$\frac{-26\times 10}{13}+26x+10+65x=5\left(6\times 13+11\right)$$
$$\frac{-260}{13}+26x+10+65x=5\left(6\times 13+11\right)$$
$$-20+26x+10+65x=5\left(6\times 13+11\right)$$
$$-10+26x+65x=5\left(6\times 13+11\right)$$
$$-10+91x=5\left(6\times 13+11\right)$$
$$-10+91x=5\left(78+11\right)$$
$$-10+91x=5\times 89$$
$$-10+91x=445$$
$$91x=445+10$$
$$91x=455$$
$$x=\frac{455}{91}$$
$$x=5$$
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