"The sole responsibility of the miracle worker is to accept the Atonement for himself. This means you recognize that mind is the only creative level, and that its errors are healed by the Atonement. Once you accept this, your mind can only heal. By denying your mind any destructive potential and reinstating its purely constructive powers, you place yourself in a position to undo the level confusion of others." - ACIM
In its fuller context, this appears to be saying that as your mind becomes healed, it becomes capable of healing, and then is in a position to be able to heal "the level confusion" of others. Jesus describes level confusion (confusion of the levels) as the sole foundation of all sickness. So that means, this gives you the power to undo the sickness of others.
What may at first seem like a focus on taking responsibility for your own Atonement, therefore extends to actual miracle working on behalf of others. Many people think that we are to only take responsibility for our own awakening and ignore the shit out of everyone else. That's how an EGO mind thinks, believing there is a separation between giving and receiving.
In the Holy Spirit's thought system what applies to you applies to everyone equally, and what is given is received. This makes the acceptance of Atonement (which is in His Mind) a different meaning - it no longer means you are accepting "exclusive" or "isolated" Atonement for a personal separate self, you're accepting that it applies to the ENTIRE sonship, and therefore that this gives you the power to heal all forms of sickness and suffering in yourself and others.
A rephrasing might be, "the sole responsibility of the person who will work miracles to heal everyone else, is to accept healing for all."
Elsewhere Jesus says "I could not atone for myself alone. Listening to one Voice implies the decision to share It in order to hear It yourself. The Mind that was in me is still irresistibly drawn to every mind created by God, because God's Wholeness is the Wholeness of His Son."