Sukkah & Taharas HaLev - A Question

I spent much of yom tov contemplating a statement in Likutey Eitzos, Moadim - Sukkos, B that states,

"Through the mitzva of sukkah a person merits taharas halev (purity of heart)."

Can anyone explain what Rebbe Nachman of Breslov meant by this? Exactly how does the mitvza of sukkah purify a person's heart?

UPDATE:

Rabbi Micha Golshevsky commented:

The Zohar Hakadosh states that there is no holiness without preparation.

We prepare by learning about the greatness of the mitzvah and begging Hashem to help us feel the holiness and purity of it.
For example, you can feel the purity of the sukkah by thinking about the fact that sukkah imparts purity and yearning to access it. This naturally leads one to beg Hashem for help attaining this.

But the more you learn about and internalize the holiness of the sukkah, the more you will feel how much you can gain through it and the more you will yearn and beg Hashem to allow you to feel the bliss of the sukkah. Of course, the more you yearn and daven the more you will feel it.

Sometimes this takes time, but if you persevere and do what you can, you will "get it." Even if you can't do much, every little bit adds up. Even just a prayer before you enter the sukkah can be very efficacious.

You are already on the right track since you are thinking about what you have learn in context of fulfilling it. If we learn something as a "vort" and not as relating to our personal avodah, it will not effect how we feel all, as discussed at very great length in sifrei mussar / machshavah / chasidus.

Here is one story that I always tell in the sukkah since it inspires me personally to yearn for the holiness of sukkah: On the first night of Sukkos, Rav Moshe of Kobrin zt”l was standing in his sukkah, profoundly moved by the holiness of the day and this special mitzvah.

He said, “The walls of the sukkah appear to be of wood, and the s’chach looks like a bunch of branches. But the truth is that every part of the sukkah embodies holy names of Hashem. Every element of the sukkah has deep kabbalistic meaning! My own Rebbe said: 'With this mitzvah we enter into holiness with our shoes on!' He meant that even the mundane human needs of the simplest Jew are transformed into lofty mitzvos through the sukkah. We eat and drink and sleep, and it is all a mitzvah!”

Hashem should help us internalize the preciousness of the sukah and remember, that even if we are far from feeling this (or had it and lost it,) we can easily access it through a little yearning and prayer. All you need to do is say with as much feeling as you can muster: "Hashem! Please grant me a taste of the sweetness of my holy and pure sukkah!"