Some 60 low-dispersion IUE spectra of the RS CVn binary V711 Tauri (K1 IV + G5 V) in the short-wavelength region, covering the interval from 1978 August to 1984 December, are available. An analysis of the complete set of spectra confirms the pattern of a long-term smooth variation of chromospheric and transition region emission which we found in an earlier study based on a selected subset of these spectra. The IUE observations reveal that a maximum in chromospheric and TR activity occurred near early 1983. However, long-term optical observations appear to indicate a minimum in spot activity at this time. We now propose a possible resolution of this puzzle based on the recent discovery by Foukal and Lean of the precise role of the solar faculae and the facular network in controling the solar irradiance. We suggest that the maximum in magnetic activity (presumably on the more active K1 star) in early 1983 which the IUE data clearly indicate, is accompanied by a maximum in starspot activity, as the solar case leads us to expect. We further assume that the visible band brightness of V711 Tau is determined by competition between the blocking effect of the dark starspots and the contributions of white-light faculae and a facular network. We propose that the observed visible band brightening of V711 Tau at activity maximum is due to the dominance of the facular and network contributions, as Foukal and Lean found to be the case for the Sun, which is brighter at solar activity maximum. We therefore propose that in V711 Tau, we are seeing an analogous effect to that observed by Foukal and Lean in the Sun, but on a greatly increased scale. The slow 10% brightness increase in V711 Tau is at least two orders of magnitude greater than the corresponding variation in solar irradiance. However, there are systematic long-term variations in the color of the system and in the Hα index, which remain difficult to interpret even if a facular component is admitted. Some of the complications may arise from contributions to these quantities from the G5 companion which contributes about 50% of the light of the system at optical wavelengths, or from global changes in the K star, or from possible contamination by gas streams. The inference of a significant facular contribution to the stellar luminosity has important consequences for spot modelling.