Here is a modified version of \sufr that now takes an optional argument indicating the raise quantity:

\documentclass[a4paper]{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\newcommand\sufr[3][0pt]{$\rule{0pt}{\dimexpr#1+1.4ex\relax}^\frac{#2}{#3}$}
\begin{document}
text$^\frac{1}{6}$ \quad text\sufr{1}{6} \quad text\sufr[5pt]{1}{6}
\end{document}
The example sets the regular sans-\sufr-style superscript fraction, followed by the regular \sufr, followed by a 5pt raise of the fraction. The default raise is 0pt, which is similar to a regular superscript fraction.
Take caution of possible line height imperfections with such use, as is shown in the following example:

\documentclass[a4paper]{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\newcommand\sufr[3][0pt]{$\rule{0pt}{\dimexpr#1+1.4ex\relax}^\frac{#2}{#3}$}
\begin{document}
The quick brown fox jumps over the lazy\sufr{1}{6} dog.
The quick brown fox jumps over the lazy\sufr{1}{6} dog.
The quick brown fox jumps over the lazy\sufr{1}{6} dog.
The quick brown fox jumps over the lazy\sufr{1}{6} dog.
The quick brown fox jumps over the lazy\sufr{1}{6} dog.
The quick brown fox jumps over the lazy\sufr{1}{6} dog.
The quick brown fox jumps over the lazy\sufr[5pt]{1}{6} dog.
The quick brown fox jumps over the lazy\sufr{1}{6} dog.
The quick brown fox jumps over the lazy\sufr{1}{6} dog.
The quick brown fox jumps over the lazy\sufr{1}{6} dog.
\end{document}
You could, of course, \smash the superscript, but that may cause overlay problems.