250 Followers Problem

Algebra Level 5

\[\log_{\sqrt{5}}{\left[\dfrac{\sqrt{(5\sqrt{5}+5)\sqrt{(5\sqrt{5}+5)^{2}\sqrt{(5\sqrt{5}+5)^{3}\sqrt{\ldots}}}}}{(6+2\sqrt{5})\sqrt[3]{215-18\sqrt[3]{215-18\sqrt[3]{215-18\sqrt[3]{\ldots}}}}}\right]}=?\]

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