Listening to the audio of TV broadcast signals can be challenging for hearing-impaired as well as normal-hearing listeners, especially when background sounds are prominent or too loud compared to the speech signal. This can result in a reduced satisfaction and increased listening effort of the listeners. Since the broadcast sound is usually premixed, we perform a subjective evaluation for quantifying the potential of speech enhancement systems based on audio source separation and recurrent neural networks (RNN). Recently, RNNs have shown promising results in the context of sound source separation and real-time signal processing. In this paper, we separate the speech from the background signals and remix the separated sounds at a higher signal-to-noise ratio. This differs from classic speech enhancement, where usually only the extracted speech signal is exploited. The subjective evaluation with 20 normal-hearing subjects on real TV-broadcast material shows that our proposed enhancement system is able to reduce the listening effort by around 2 points on a 13-point listening effort rating scale and increases the perceived sound quality compared to the original mixture.