[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 $M_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ in any band $\gtrsim <!--\; ???\; -->-<!--\; ???\; -->19.5$ mag, while the ⁵⁶Ni can be neglected in fitting most type Ic superluminous supernovae whose $M_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ in any band is $\lesssim <!--\; ???\; -->-<!--\; ???\; -->21$ mag, since the luminosity from a magnetar (highly magnetized NS) can outshine that from a moderate amount of ⁵⁶Ni. For luminous SNe Ic with $-<!--\; ???\; -->21\lesssim <!--\; ???\; -->M_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}\lesssim <!--\; ???\; -->-<!--\; ???\; -->19.5$ 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 $\sim <!--\; ???\; -->0.5M_{\odot <!--\; ???\; -->}$. 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 $M_{\mathrm{N}\mathrm{i}}$ to $M_{\mathrm{e}\mathrm{j}}$ 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.