1 Peter 5 makes much clearer what it means to commit one's way to the Lord: Casting all of your cares on Him because He cares. What is in view here is not just an aspect of your life, but the totality of it. God wants to help us, but He can only do so to the extent that we let go of our claims of being able to do it for ourselves. We have to come to the place where we agree with Jesus that we can do nothing without Him.
Whatever we believe we can do without Christ comes in our way to receiving true help from God who wants to help us. In Matthew 11:28, Jesus invites all who labour and are heavily burdened, to come to Him for rest. But it is one thing to come to Christ, it is entirely another thing to cast all our burdens on Him, which is the expression of our dependence on Him.
When we come to Christ and continue to bear the burdens of our lives on us, we are like a person who boards the bus, and yet, carries his load on his head. The fare paid covers for the luggage we bring on board. The same is true of when we come to Christ, the price that He paid for our redemption covers everything in our lives. It covers the baggage of life's distress that we bring along with us to Him, therefore, He calls on all who come to Him to cast all, not some, bur all of their burdens upon Him, because He cares for them.
Toni