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To fight climate change and accommodate the increasing population, global crop production has to be strengthened. To achieve the "sustainable intensification" of agriculture, transforming it from carbon emitter to carbon sink is a priority, and understanding the environmental impact of agricultural management practices is a fundamental prerequisite to that. At the same time, the global agricultural landscape is deeply heterogeneous, with differences in climate, soil, and land use inducing variations in how agricultural systems respond to farmer actions. The "personalization" of sustainable agriculture with the provision of locally adapted management advice is thus a necessary condition for the efficient uplift of green metrics, and an integral development in imminent policies. Here, we formulate personalized sustainable agriculture as a Conditional Average Treatment Effect estimation task and use Causal Machine Learning for tackling it. Leveraging climate data, land use information and employing Double Machine Learning, we estimate the heterogeneous effect of sustainable practices on the field-level Soil Organic Carbon content in Lithuania. We thus provide a data-driven perspective for targeting sustainable practices and effectively expanding the global carbon sink.