Japan | A beautiful Olympiad Exponential Trick | 5^(m+6) = 6^(m+5)

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Without so much ado:
5 E (m + 6) = 6 E (m + 5)
(m + 6) lg 5 = (m + 5) lg 6 | lg = log to the base of 10
(m + 6 ) / (m + 5) = lg 6 / lg5 | lg 6 / lg 5 = a ~ 1,113
(m + 6) / (m + 5) = a
m + 6 = a * (m + 5)
m + 6 = am + 5a
m - am = 5a - 6
m (1 - a) = (5a - 6)
m = (5a - 6) / (1 - a) | ~ 3,827
5 E (m + 6) ~ 7.397.860,423
6 E (m + 5) ~ 7.397.860,423