Artificial Intelligence (AI) has advanced significantly in various domains like healthcare, finance, and cybersecurity, with successes such as DeepMind's medical imaging and Tesla's autonomous vehicles. As telecommunications transition from 5G to 6G, integrating AI is crucial for complex demands like data processing, network optimization, and security. Despite ongoing research, there's a gap in consolidating AI-enabled Spectrum Management (AISM) advancements. Traditional spectrum management methods are inadequate for 6G due to its dynamic and complex demands, making AI essential for spectrum optimization, security, and network efficiency. This study aims to address this gap by: (i) Conducting a systematic review of AISM methodologies, focusing on learning models, data handling techniques, and performance metrics. (ii) Examining security and privacy concerns related to AI and traditional network threats within AISM contexts. Using the Systematic Literature Review (SLR) methodology, we meticulously analyzed 110 primary studies to: (a) Identify AI's utility in spectrum management. (b) Develop a taxonomy of AI approaches. (c) Classify datasets and performance metrics used. (d) Detail security and privacy threats and countermeasures. Our findings reveal challenges such as under-explored AI usage in critical AISM systems, computational resource demands, transparency issues, the need for real-world datasets, imbalances in security and privacy research, and the absence of testbeds, benchmarks, and security analysis tools. Addressing these challenges is vital for maximizing AI's potential in advancing 6G technology.