$$m - \frac { m - 1 } { 2 } = 1 \frac { \sqrt { 13 } } { 3 }$$
$m=\frac{2\sqrt{13}}{3}-1\approx 1.40370085$
$$6m-3\left(m-1\right)=2\sqrt{13}$$
$$6m-3m+3=2\sqrt{13}$$
$$3m+3=2\sqrt{13}$$
$$3m=2\sqrt{13}-3$$
$$\frac{3m}{3}=\frac{2\sqrt{13}-3}{3}$$
$$m=\frac{2\sqrt{13}-3}{3}$$
$$m=\frac{2\sqrt{13}}{3}-1$$
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