In traditional chaos shift keying (CSK) communication systems, implementing chaotic synchronization techniques is costly but practically unattainable in a noisy environment. This paper proposes a combined chaotic sequences-based $M$-ary CSK (CCS-$M$-CSK) system that eliminates the need for chaotic synchronization. At the transmitter, the chaotic sequence is constructed by combining two chaotic segments of different lengths, where each is generated from distinct chaotic systems and only one kind of chaotic segment modulates the information signal. At the receiver, a deep learning unit with binary classification is meticulously designed to recover information symbols. The symbol error rate (SER) performance of the proposed system is evaluated over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. Specifically, the impact of varying misalignment lengths on the SER performance of the system is analyzed when the received sequence is misaligned. Furthermore, the proposed system demonstrates significant performance advantages over existing CSK-based systems in multipath Rayleigh fading channels. These features establish CCS-$M$-CSK as a promising candidate for various applications, including Vehicle-to-Everything (V2X).