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Digital advertising constitutes one of the main revenue sources for online platforms. In recent years, some advertisers tend to adopt auto-bidding tools to facilitate advertising performance optimization, making the classical \emph{utility maximizer} model in auction theory not fit well. Some recent studies proposed a new model, called \emph{value maximizer}, for auto-bidding advertisers with return-on-investment (ROI) constraints. However, the model of either utility maximizer or value maximizer could only characterize partial advertisers in real-world advertising platforms. In a mixed environment where utility maximizers and value maximizers coexist, the truthful ad auction design would be challenging since bidders could manipulate both their values and affiliated classes, leading to a multi-parameter mechanism design problem. In this work, we address this issue by proposing a payment rule which combines the corresponding ones in classical VCG and GSP mechanisms in a novel way. Based on this payment rule, we propose a truthful auction mechanism with an approximation ratio of $2$ on social welfare, which is close to the lower bound of at least $\frac{5}{4}$ that we also prove. The designed auction mechanism is a generalization of VCG for utility maximizers and GSP for value maximizers.