We study the one-dimensional quantum Heisenberg ferromagnet with exchange couplings exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{alpha}$, where $k$ is the wave-vector of the modulations on the random coupling landscape. By using renormalization group, integration of the equations of motion and exact diagonalization, we compute the spin-wave localization length and the mean-square displacement of the wave-packet. We find that, associated with the emergence of extended spin-waves in the low-energy region for $alpha > 1$, the wave-packet mean-square displacement changes from a long-time super-diffusive behavior for $alpha <1$ to a long-time ballistic behavior for $alpha > 1$. At the vicinity of $alpha =1$, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as $E_cpropto (alpha -1)^{1/3}$.
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