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Recent observations indicate that galactic outflows are ubiquitous in high redshift galaxies, including normal star forming galaxies, quasar hosts, and dusty star forming galaxies (DSFGs). However, the impact of outflows on the evolution of their hosts is still an open question. Here, we analyse the star formation histories (SFH) and galactic outflow properties of galaxies in massive haloes ($10^{12}M_{\odot}<M_{\rm vir} <5\times 10^{12}M_{\odot}$) at $z\gtrsim5.5$ in three zoom-in cosmological simulations from the MassiveFIRE suite, as part of the Feedback In Realistic Environments (FIRE) project. The simulations were run with the FIRE-2 model, which does not include feedback from active galactic nuclei (AGN). The simulated galaxies resemble $z>4$ DSFGs, with SFRs of $\sim 1000\ M_{\odot}\rm yr^{-1}$ and molecular gas masses of $M_{\rm mol}\sim 10^{10}\ M_{\odot}$. However, the simulated galaxies are characterised by higher circular velocities than those observed in high-z DSFGs. The mass loading factors from stellar feedback are of the order of $\sim 0.1$, implying that stellar feedback is inefficient in driving galactic outflows and gas is consumed by star formation on much shorter time-scales than it is expelled from the interstellar medium (ISM). We also find that stellar feedback is highly inefficient in self-regulating star formation in this regime, with an average integrated star formation efficiency (SFE) per dynamical time of $30\%$. Finally, compared to FIRE-2 galaxies hosted in similarly massive haloes at lower redshift, we find lower mass loading factors and higher SFEs in the high redshift sample. We argue that both effects originate from the higher total and gas surface densities that characterise high$-z$ massive systems.