In clustered data such as the United Network of Organ Sharing (UNOS) database, the center size can affect patient survival time after transplant with its access to medical resources. Improper statistical procedures to handle informative cluster size can lead to biased results and misleading inferences. While the accelerated failure time (AFT) mixture cure model and the Cox proportional hazards (PH) mixture cure model are two classic models to analyze clustered survival data, the AFT has attracted less attention than its semiparametric counterpart due to the complexity of the estimation method. However, its direct physical interpretation and developments to the rank-based generalized estimating equations (GEE) provides an incentive to use for censored failure time data. We propose a new estimation method for the semiparametric AFT mixture cure model that employs a faster expectation-maximization (EM) algorithm, the SQUAREM, that can accelerate any fixed-point and smooth mapping with linear convergence rate and an induced smoothing inverse cluster size reweighting procedure to handle the informative cluster size. We apply proposed method to kidney transplant data in UNOS.