Evaluate the sum
$\sum_{k=0}^{\infty}\left(3\cdot\frac{\ln(4k+2)}{4k+2}-\frac{\ln(4k+3)}{4k+3}-\frac{\ln(4k+4)}{4k+4}-\frac{\ln(4k+5)}{4k+5}\right)$
$=3\cdot\frac{\ln2}{2}-\frac{\ln3}{3}-\frac{\ln4}{4}-\frac{\ln5}{5}+3\cdot\frac{\ln6}{6}-\frac{\ln7}{7}-\frac{\ln8}{8}-\frac{\ln9}{9}+3\cdot\frac{\ln10}{10}-\cdots.$
(As usual, $lnx$ denotes the natural logarithm of x.)
 The original answer is in $(\log m)^{n}$format, please give the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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