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[en] Most type Ic core-collapse supernovae produce 56Ni and neutron stars (NSs) or black holes. The dipole radiation of nascent NSs has usually been neglected in explaining supernovae (SNe) with peak absolute magnitudes in any band mag, while the 56Ni can be neglected in fitting most type Ic superluminous supernovae whose in any band is mag, since the luminosity from a magnetar (highly magnetized NS) can outshine that from a moderate amount of 56Ni. For luminous SNe Ic with mag, however, both contributions from 56Ni and NSs cannot be neglected without serious modeling since they are not SLSNe and the 56Ni mass could be up to . In this paper we propose a unified model that contains contributions from both 56Ni and a nascent NS. We select three luminous SNe Ic-broad-lined, SN 2010ay, SN 2006nx, and SN 14475, and show that, if these SNe are powered by 56Ni, the ratio of to is unrealistic. Alternatively, we invoke the magnetar model and the hybrid (56Ni + NS) model and find that they can fit the observations, indicating that our models are valid and necessary for luminous SNe Ic. Owing to the lack of late-time photometric data, we cannot break the parameter degeneracy and thus distinguish among the model parameters, but we can expect that future multi-epoch observations of luminous SNe can provide stringent constraints on 56Ni yields and the parameters of putative magnetars.