Automated Essay Scoring (AES) using neural networks has helped increase the accuracy and efficiency of scoring students' written tasks. Generally, the improved accuracy of neural network approaches has been attributed to the use of modern word embedding techniques. However, which word embedding techniques produce higher accuracy in AES systems with neural networks is still unclear. In addition, the importance of fine-tuned word embedding techniques on the accuracy of the AES systems is not justified yet. This study investigates the effect of fine-tuned modern word embedding techniques, including pretrained GloVe and Word2Vec, on the accuracy of a deep learning AES model using a Long-Short Term Memory (LSTM) network. The dataset used in this study consisted of 12,978 essays introduced in the 2012 Automated Scoring Assessment Prize (ASAP) competition. Results show that fine-tuned word embedding techniques could significantly improve the accuracy of the AES (QWK= 0.79) compared with the baseline model without pretrained embeddings (QWK = 0.73). Moreover, when used in AES, the pre-trained GloVe word embedding (QWK= 0.79) outperformed Word2Vec (QWK = 0.77). The results of this study can guide future AES studies in selecting more appropriate word representations and how to fine-tune the word embedding techniques for scoring-related tasks.