The elder brother said to the younger brother, when I was your age, you were still in kindergarten. The younger brother said to the elder brother, when I was your age, you had already graduated from college. The elder brother said to the younger brother, when I was your age, your age was exactly a square number. The younger brother said to the elder brother, when I was your age, your age was also a square number. If the elder brother and younger brother are all enrolled at the age of 6 and have not skipped a grade, what is the minimum age of their sum?
哥哥对弟弟说，我在你现在这么大时，你还在读幼儿园．弟弟对哥哥说，我到你现在这么大时，你已经大学毕业．哥哥对弟弟说，我在你现在这么大时，你的年龄正好是一个平方数．弟弟对哥哥说，我到你现在这么大时，你的年龄也是一个平方数．如果哥哥弟弟都是6岁入学，且未跳级，那么他们的年龄之和至少多少岁？
<gadget id="calculator">4 + 7</gadget>
<output>11</output>

<gadget id="calculator">11 + 7</gadget>
<output>18</output>

<gadget id="calculator">11 + 18</gadget>
<output>29</output>

<result>29</result>