The formalism of structural causal models provides a precise approach for describing certain types of distribution shifts, via the notion of a soft intervention or mechanism change. Popular approaches to learning causal structure from data rely on the availability of distribution shifts in order to identify between otherwise indistinguishable models. However, many approaches rely on prior knowledge of which variables have been shifted between settings, called intervention targets. When this information is not available, one must simultaneously learn both intervention targets and the causal structure. We introduce the Unknown-Target Interventional Greedy Sparsest Permutation algorithm, a nonparametric, hybrid approach for this learning task. We prove the consistency of the algorithm, and demonstrate its performance on synthetic and biological datasets.