As online conversations become more prevalent, achieving genuine understanding across cultures remains a significant challenge. This study draws on Communication Accommodation Theory and Digital Nudging from behavioral economics to examine whether real-time LLM-generated nudges can enhance authenticity and mutual understanding during online interactions between users. Employing a controlled, mixed factorial experimental design, the research evaluates culturally adaptive LLMs feedback interventions within task-based chat scenarios. Preliminary findings showed the existence of misperceptions in digital communication. Previous empirical studies, conducted by the author and involving 599 participants from Arab and British user groups, have revealed distinct cultural preferences in communication styles and showed the existence of misperceptions. The proposed intervention in this proposal uses LLM-generated personalized feedback and digital nudges to help users recognize and adapt their communication styles in real time, so that it helps more compatibility amongst communicating parties. Results from this work are expected to provide actionable guidance for developers and researchers in behavioral and social computing, supporting the creation of more inclusive and authentic digital communities.