The article presents the results of an experimental study to establish the leaching indicators for limestone-kaolin cakes conducted using soda solutions with various process parameters. The experiments use the mathematical planning method that allows assessing the significance of various cake leaching parameters with the minimum number of experiments. It is shown that the temperature and concentration of the soda solution have a significant effect on the aluminum oxide recovery, with the highest recovery of 79.5 % within the selected factor variation intervals achieved at the process temperature of 50 °C, the soda solution concentration of 100 g/l, the liquid/solid ratio in the slurry of 7, and the leaching time of 25 minutes. Further studies using the coordinate-wise optimization method allowed establishing the leaching process parameters that ensure the aluminum oxide recovery of up to 85.2 %. At the same time, the paper shows a significant effect of the process temperature and time on the depth of secondary interactions leading to the deposition of aluminum oxide and requiring additional systemic studies. The established chemical and material composition of the sludge suggests that it may be effectively used as a component in raw Portland cement mixes, as well as a raw material for the regeneration and recycling of the lime component, which would reduce the consumption of natural carbonate raw materials and cut the emissions of greenhouse gases into the atmosphere. The research was carried out with the use of the laboratory equipment of the Scientific and Educational Center for Shared Use of the St. Petersburg Mining University. The work was carried out with the financial support of the Russian Science Foundation under the Agreement No. 18-19-00577 of April 26 2018 of grant for fundamental scientific research and exploratory scientific research.