Jesus came to preach the gospel, but he also came to "succor his people" (Alma 7:12). He not only preached the gospel, he healed the lame, the infirm, the deaf, and the blind. It is not too much to suggest that preaching the gospel and succoring those who sorrow and suffer were not two things but one, the one act of God's divine condescension to love and save us.
All human sorrow, whether visible or hidden, needs God's grace. It also needs ours. Of course it needs our graceful acts of charity and compassion, but more than that human sorrow needs our repentance, a change in our orientation within the world and among our fellows.
So as we fast, we should not only pray for specific blessings on specific others and on those whose sorrow remains undiscovered. We must also ask God to change our hearts so that we see the world as a place of suffering—not as a dismal place, but as a place in which others sorrow in ways that I do not know and to which I must nevertheless respond in Christian love.