Summary: In this work, we determine explicitly the set of algebraic points of degree at most 3 over \(\mathbb{Q}\) on the affine curve \(\mathcal{C}_3(11):y^{11}=x^3(x-1)^3\). This result is a special case of quotients of Fermat curves \(\mathcal{C}_{r,s}(p):y^p=x^r(x-1)^s\), \(1\le r,s,r+s\le p-1\) for \(p=11\) and \(r=s=3\). The results obtained extend the work of Gross and Rohrlich who determined \(\bigcup_{[\mathbb{K}:\mathbb{Q}]\le2}\mathcal{C}_1(11)(\mathbb{K})\) the set of algebraic points on \(\mathcal{C}_1(11)\) of degree at most 2 on \(\mathbb{Q}\).