Nested Roots Problem

Algebra Level pending

Round \(x\) to the nearest ones place: \[\left (\sqrt[3]{9\sqrt[3]{7\sqrt[3]{9\sqrt[3]{7\cdots}}}} \right )^{3}+\left (\sqrt[4]{8\sqrt[4]{6\sqrt[4]{8\sqrt[4]{6\cdots}}}} \right )^{2}=x\]


First off, I must give credit for inspiring this problem to Nxin Nasn, whose original problem is here.
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