Young adults often encounter challenges in career exploration. Self-guided interventions, such as the letter-exchange exercise, where participants envision and adopt the perspective of their future selves by exchanging letters with their envisioned future selves, can support career development. However, the broader adoption of such interventions may be limited without structured guidance. To address this, we integrated Large Language Model (LLM)-based agents that simulate participants' future selves into the letter-exchange exercise and evaluated their effectiveness. A one-week experiment (N=36) compared three conditions: (1) participants manually writing replies to themselves from the perspective of their future selves (baseline), (2) future-self agents generating letters to participants, and (3) future-self agents engaging in chat conversations with participants. Results indicated that exchanging letters with future-self agents enhanced participants' engagement during the exercise, while overall benefits of the intervention on future orientation, career self-concept, and psychological support remained comparable across conditions. We discuss design implications for AI-augmented interventions for supporting young adults' career exploration.