How do I test local inner class methods in java?

In many application I often have algorithms which make use of dedicated sub-algorithms (or simply well defined pieces of code).

Till now, when I wrote the main algorithm, i created a private method for each sub-algorithm like in the example below (OldStyle):

public class OldStyle {

    public int mainAlg() {
        int x = subAlg01();
        int y = subAlg02();
        int z = x * y;
        return z;
    }

    private int subAlg01() {
        return 3;
    }

    private int subAlg02() {
        return 5;
    }
}

This worked fine but I didn't like having a proliferation of methods (subAlg01 and subAlg02) which, even if private, were only used by one method (mainAlg).

Recently I dicovered the use of local inner classes and now my example is (NewStyle):

public class NewStyle {

    public int mainAlg() {
        class Nested {

            public int subAlg01() {
                return 3;
            }

            public int subAlg02() {
                return 5;
            }
        }
        Nested n = new Nested();
        int x = n.subAlg01();
        int y = n.subAlg02();
        int z = x * y;
        return z;
    }
}

I like it very much but now I have the following problem: how do I test subAlg01 and subAlg02 using JUnit?

By the way: I'm using eclipse.

Thanks for you help.

Edit: I try to explain better: I have, let's say, a sorting algorithm and I want to test it to be sure it runs as expected. This sorting algorithms is used by only method m of class X. I could make it a private method of class X but class X usually has nothing to do with sorting, so why "spoil" class X with the sorting method? So I put it inside method m. Some time later I want to improve my sorting algorithm (I make it faster) but I want to be sure that it's behavior is as expected, so I want to re-test it with the original tests.

That's what I want to do, maybe there is no solution, I hope someone may help me.

Edit after answer choice. I selected Rodney answer because his solution is the one I adopted: a standalone helper class helps me (it's a helper!) to have a clear view of what are the sub methods and it also gives me the ability to test them.