Two new research facilities will be ready for operation very soon (MEGa-Ray at Liver-more National Laboratory) or start construction (ELI-Nuclear Physics in Bucharest), both providing highly brilliant γ beams with so far unprecedented properties via Compton backscattering of laser photons from a high-quality, relativistic electron beam. With these intense, monochromatic γ beams, a new era of photonuclear physics will be enabled. A new research campaign is proposed to exploit the unprecedented properties of these highly-brilliant, novel γ beams on highly-selective studies of extremely deformed nuclei in the multiple-humped potential energy landscape of the actinides via photofission. With the unique γ beam bandwidth of ΔE/E=10-3, we can aim at resolving individual resonances which could never be achieved so far due to the limited γ bandwidth of bremsstrahlung beams. Exploratory, non-bremsstrahlung photofission experiments are going to be performed very soon at the HIγS facility (Duke University, USA) to investigate the fine structure of the sub-barrier transmission resonances of the actinides.