Rumi and Plato

I've noticed a huge similarity between Rumi's poems and Plato's Allegory of a Cave. The idea that truth cannot be gathered from the objects around us, which are worldly and can only be understood by the five senses. Rumi emphasizes the idea in his poems that we do not see truth because we are too distracted by worldly things and ideas, that we must empty our souls of all distractions and look within ourselves to find truth and God. Likewise, Plato states that what we perceive through the five senses is false and that truth can only be reached through one's intellect, which is also only reserved to the individual and not his or her surroundings. Using one's intellect in this sense therefore implies that one has discarded all other considerations and utilized what's inside, whether it be the reason of intellect or the tranquility of the soul, to arrive at truth.