Disagreements are common in online societal deliberation and may be crucial for effective collaboration, for instance in helping users understand opposing viewpoints. Although there exist automated methods for recognizing disagreement, a deeper understanding of factors that influence disagreement is currently missing. We investigate a hypothesis that differences in personal values influence disagreement in online discussions. Using Large Language Models (LLMs) for estimating both profiles of personal values and disagreement, we conduct a large-scale experiment involving 11.4M user comments. We find that the dissimilarity of value profiles correlates with disagreement only in specific cases, but that incorporating self-reported value profiles changes these results to be more undecided.