The power consumption of the analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) in fully digital massive multiple-input multiple-output (MIMO) systems motivates the adoption of low-resolution architectures. In particular, 1-bit DACs reduce the power consumption and hardware complexity at the transmitter, but introduce severe transmit-side quantization distortion. In this paper, we investigate data detection for a point-to-point massive MIMO system with 1-bit DACs at the transmitter, where the linearly precoded signal is dithered prior to quantization, and either full-resolution or 1-bit ADCs at the receiver. Assuming that the dither vector applied at the transmitter is known at the receiver, we first develop softestimation-based data detection methods with symbol-independent dither removal for both full-resolution and 1-bit ADCs. We then introduce a new symbol-dependent linearization of the transmitted signal at the output of the 1-bit DACs and use it to derive maximum-likelihood (ML)-based data detection methods that directly recover the data symbol vector from the received signal. For full-resolution ADCs, this leads to an ML-based method with and without dither removal. For 1-bit ADCs, we develop an approximate ML-based method that exploits the derived statistics of the received signal without dither removal. We also propose low-complexity variants of the ML-based methods to mitigate the exponential complexity growth with the number of streams. Numerical results in terms of symbol error rate highlight the critical role of the dither power and demonstrate that the proposed ML-based methods (along with their low-complexity variants) achieve significant gains over a baseline based on binary ML detection via a homotopy algorithm.