Among the smart capabilities promised by the next generation cellular networks (5G and beyond), it is fundamental that potential network anomalies are detected and timely treated to avoid critical issues concerning network performance, security, public safety. In this paper, we propose a comprehensive framework for detecting network anomalies using mobile traffic data: collecting data from the LTE Physical Downlink Control Channel (PDCCH) of different eNodeBs, we implement deep learning algorithms in a semi-supervised way to detect potential traffic anomalies that are generated, for example, by unexpected crowd gathering. With respect to other types of mobile dataset, using LTE PDCCH information, we are able to obtain fine-grained and high-resolution data for the users that are connected to the LTE eNodeB. Through a semi-supervised approach, algorithms are trained to detect anomalies using only one class of traffic samples. We design two algorithms based on stacked-LSTM Neural Networks: 1) LSTM Autoencoder (LSTM-AE), in which the objective is to reconstruct the traffic samples 2) LSTM traffic predictor (LSTM-PRED), where the goal is to predict the traffic in the next time-instants, based on historical data. In both cases, we analyze the reconstruction (or prediction) error to assess if the mobile traffic presents anomalies or not. Using the F1-score as metric, we demonstrate that the proposed methods are able to identify the anomalous traffic periods, beating a benchmark that comprises different state-of-the-art algorithms for anomaly detection.