In John 6:35, Jesus is teaching that upon coming to him, the bread of life, in faith, one will never have to search anywhere else again for sustenance. This is clearly not referring to physical hunger and thirst, and to miss the spiritual emphasis of these words is to make the identical error the people hearing Jesus are making. In fact, having this hunger and thirst of the soul quenched, enables one to be full, despite the lack of tangible blessings. 

One way you can spot someone who understands the significance of v.35 is when come across those who are going through a trial, but say something like this—“Yeah this is hard, but I know I have feasted on the bread of life and if all I have is Christ, that is sufficient.”

Now you might be saying—“I can’t testify to that. I find myself consumed with earthly circumstances and then I constantly worry about them.” At this point, we just have to go back to Jesus’ prohibition in v.27—Stop spending yourself for food that perishes. Stop placing your trust in changed circumstances. Stop substituting the bread of life for bread that will rot sooner rather than later.