Through numerical simulations, we demonstrate the existence of an infinite family of temporal cavity solitons (CSs), which balance arbitrary negative pure, even-order dispersion k and self-phase modulation, as well as loss and parametric gain. These correspond to frequency combs with increasingly flatter spectra as k increases. We determine the analytic forms of these solitons at high pump power and detuning and derive that their energy is related to the pulse duration Δτ as Δτ−(k−1).