The advent of ultra-massive multiple-input-multiple output systems holds great promise for next-generation communications, yet their channels exhibit hybrid far- and near- field beam-squint (HFBS) effect. In this paper, we not only overcome but also harness the HFBS effect to propose an integrated location sensing and communication (ILSC) framework. During the uplink training stage, user terminals (UTs) transmit reference signals for simultaneous channel estimation and location sensing. This stage leverages an elaborately designed hybrid-field projection matrix to overcome the HFBS effect and estimate the channel in compressive manner. Subsequently, the scatterers' locations can be sensed from the spherical wavefront based on the channel estimation results. By treating the sensed scatterers as virtual anchors, we employ a weighted least-squares approach to derive UT' s location. Moreover, we propose an iterative refinement mechanism, which utilizes the accurately estimated time difference of arrival of multipath components to enhance location sensing precision. In the following downlink data transmission stage, we leverage the acquired location information to further optimize the hybrid beamformer, which combines the beam broadening and focusing to mitigate the spectral efficiency degradation resulted from the HFBS effect. Extensive simulation experiments demonstrate that the proposed ILSC scheme has superior location sensing and communication performance than conventional methods.