Recent studies showed that network slices (NSs), which are logical networks supported by shared physical networks, can experience service interference due to sharing of physical and virtual resources. Thus, from the perspective of providing end-to-end (E2E) service quality assurance in 5G/6G systems, it is crucial to discover possible service interference among the NSs in a timely manner and isolate the potential issues before they can lead to violations of service quality agreements. We study the problem of detecting service interference among NSs in 5G/6G systems, only using E2E key performance indicator measurements, and propose a new algorithm. Our numerical studies demonstrate that, even when the service interference among NSs is weak to moderate, provided that a reasonable number of measurements are available, the proposed algorithm can correctly identify most of shared resources that can cause service interference among the NSs that utilize the shared resources.