The data sample of Λ0b→J/ψpK− decays acquired with the LHCb detector from 7 and 8 TeV pp collisions, corresponding to an integrated luminosity of 3 fb−1, is inspected for the presence of J/ψp or J/ψK− contributions with minimal assumptions about K−p contributions. It is demonstrated at more than nine standard deviations that Λ0b→J/ψpK− decays cannot be described with K−p contributions alone, and that J/ψp contributions play a dominant role in this incompatibility. These model-independent results support the previously obtained model-dependent evidence for P+c→J/ψp charmonium-pentaquark states in the same data sample.Received 19 April 2016DOI:https://doi.org/10.1103/PhysRevLett.117.082002This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.© 2016 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)Research AreasQuark modelPhysical SystemsExotic baryonsParticles & Fields