Accurate and timely information on dam-break waves is essential for risk assessment and disaster mitigation. The unsteady flow interacting with in-channel obstacles renders numerical simulations computationally costly. This study establishes a machine learning (ML)-enhanced reduced-order model (ROM), which provides accelerated and accurate flow predictions. The model consists of three phases: dimensionality reduction, long short-term memory (LSTM) optimization and forecasting, and flow field reconstruction. The proper orthogonal decomposition (POD) first reduces the complexity of the physical system while maintaining the dominant flow dynamics. Subsequently, an LSTM fine-tuned by the grey wolf optimization (GWO) predicts the evolution of the POD coefficients in the reduced-order space. Lastly, the flow field is reconstructed using the high-energy POD modes and the estimated amplitudes. The proposed GWO-LSTM-ROM is evaluated for time-dependent dam-break flows in a wetted channel with obstacles. Based on the comparison of millions of data samples, the approach is highly consistent with the high-fidelity full-order model, with a coefficient of determination over 0.99. Meanwhile, the average computational efficiency is improved by 86%. The main contribution of this work is to develop an improved method for fast and accurate modeling of complex flows, benefiting a wide range of applications, e.g., multiphase flows and fluid-structure interactions.