Solve the reccurence $T(n) = 3T(\sqrt[3]{n}) + \log_{2}(\log_{2}n)$

Question

$T(1) = 1 $ ,

$T(n) = 3T(\sqrt[3]{n}) + \log_{2}(\log_{2}n)$.

I tried to define $ n = 2^{k}$.

So, $T(2^k) = 3T(2^{\frac{k}{3}}) + \log_{2}k$

Then defin $S(k) = T(2^k)$

So ,$S(k) = 3S(\frac{k}{3}) + \log_{2}k$

And now im pretty stuck, Someone has an idea ? Thanks.