ALMA observations have revealed that [CII] 158μm line emission in high-z galaxies is ~2-3× more extended than the UV continuum emission. Here we explore whether surface brightness dimming (SBD) of the [CII] line is responsible for the reported [CII] deficit, and the large L[OIII]/L[CII] luminosity ratio measured in early galaxies. We first analyse archival ALMA images of nine z>6 galaxies observed in both [CII] and [OIII]. After performing several uv-tapering experiments to optimize the identification of extended line emission, we detect [CII] emission in the whole sample, with an extent systematically larger than the [CII] emission. Next, we use interferometric simulations to study the effect of SBD on the line luminosity estimate. About 40% of the extended [CII] component might be missed at an angular resolution of 0.8′′, implying that L[CII] is underestimated by a factor ≈2 in data at low (<7) signal-to-noise ratio . By combining these results, we conclude that L[CII] of z>6 galaxies lies, on average, slightly below the local L[CII]−SFR relation (Δz=6−9=−0.07±0.3), but within the intrinsic dispersion of the relation. SBD correction also yields L[OIII]/L[CII]<10, i.e. more in line with current hydrodynamical simulations.